Saurabh Dubey

What is the error in this ?

x=1+2+4+8+16+32+........

x-1=2+4+8+16+32+......

x-1=2(1+2+4+8+16+......)

x-1=2x

x=-1

please explain...

Thanks in advance !

Prove that for arbitrary real positive numbers following inequality holds

(1/a) + (1/b) + (1/c) ≤ (a^8 + b^8 + c^8 )/(a^3. b^3. c^3)

In a quadrilateral ABCD , It is given that

∠ BAC = ∠CAD = x

∠BDC = ∠ACB = y

∠ADB = 90°

Then find y= ?

The least possible number of positive roots of the equation 2x^7 - x^4 + 4x^3 - 5 = 0 is .....?

please explain ..

Thanks in advance

The number of distinct real roots of the equation

x^9 + x^7 + x ^ 5 + x ^3 + x ^2 + 1= 0

How to approach these kinds of problems . Explain me please .

Thanks in advance .

If vector F =(x²+y-4) i^ + (3xy) j^ +( 2xz + z²) k^ ,

then evaluate the surface integral

∫ ∫ (∇ × F).n^ dS

S

Where S is the surface of the cone

z=1-√(x²+y²) lying above xy - plane and n^ is the unit normal to S making an acute angle with k^.

Please also show the steps .

Thanks in advance !

Let P and Q be two real matrices of size (4×6) and (5×4) respectively. If rank (Q)=4 and

rank(QP)= 2, then rank(P) = ??

please explain

Thanks in advance !

E and F are the interior points on side BC and CD of a parallelogram ABCD. Let (vector BE) = 4 (vector EC)

and ( vector CF) = (vector FD) .If the lines EF meets the diagonal AC in G , then (vector AG) =λ (vector AC )

Then λ = ?

Please help me Math Experts....

Thanks in advance !

Is f(x,y)= x² - x√y continuous and differentiable at ( 0,0)

?

please explain the method for checking continuity and differentiability of this two variable function

Thanks in advance

If log_0.3 ( x-1) < log_0.09(x-1)

then x lies in the interval....(....,...).......?

Please show all steps....

Thanks in advance

If ax + hy + gz = 0, hx + by + fz = 0, gx + fy + cz = 0, Then prove that :

x²/(bc – f²) = y²/(ca – g²) = z²/(ab – h²) ....

Please tell me any smart method to prove it...

Thanks in advance ...

If x= cy + bz , y= az + cx , z = bx + ay

Then prove that :

x^2/(1-a^2) = y^2/(1-b^2)=z^2/(1-c^2)

Thanks in advance....

Let P and Q be two real matrices of size (4×6) and (5×4) respectively. If rank (Q)=4 and

rank(QP)=  2, then rank(P) = ??

Please explain

Let a,b,c,d be distinct non-zero real numbers with (a + b) = (c + d).Then an eigenvalue of the matrix

[ a b 1 ].....1st row

| c d 1|......2nd row

[ 1 -1 0]......3rd row

1) a+c

2)a+b

3)a-b

4)b-d